def L6_32(F, a): sc = { ('X_1', 'X_2'): { 'X_3': 1 }, ('X_1', 'X_3'): { 'X_4': 1 }, ('X_1', 'X_4'): { 'X_5': 1 }, ('X_2', 'X_3'): { 'X_6': a }, ('X_2', 'X_5'): { 'X_6': 1 }, ('X_3', 'X_4'): { 'X_6': 1 } } return ClassifiedNilpotentLieAlgebra( F, 'L6_32(%s)' % (a), sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L6_21(F, a): # classification in GAP follows Cicalo-de Graaf-Schneider 2012 # instead of the slightly different de Graaf 2007 # the only differences are: # L6_19(0) -> L6_27 # L6_21(0) -> L6_28 if a == F.zero(): return L6_28(F) sc = { ('X_1', 'X_2'): { 'X_3': 1 }, ('X_1', 'X_3'): { 'X_4': 1 }, ('X_1', 'X_4'): { 'X_6': 1 }, ('X_2', 'X_3'): { 'X_5': 1 }, ('X_2', 'X_5'): { 'X_6': a } } return ClassifiedNilpotentLieAlgebra( F, 'L6_21(%s)' % (a), sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L5_8(F): sc = { ('X_1', 'X_2'): {'X_4': 1}, ('X_1', 'X_3'): {'X_5': 1} } return ClassifiedNilpotentLieAlgebra(F, 'L5_8', sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5'])
def L6_27(F): sc = { ('X_1', 'X_2'): { 'X_3': 1 }, ('X_1', 'X_3'): { 'X_5': 1 }, ('X_2', 'X_4'): { 'X_6': 1 } } return ClassifiedNilpotentLieAlgebra( F, 'L6_27', sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L6_1(F): sc = {} return ClassifiedNilpotentLieAlgebra( F, 'L6_1', sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L1_1(F): sc = {} return ClassifiedNilpotentLieAlgebra(F, 'L1_1', sc, names=['X_1'])
def L3_2(F): sc = {('X_1', 'X_2'): {'X_3': 1}} return ClassifiedNilpotentLieAlgebra(F, 'L3_2', sc, names=['X_1', 'X_2', 'X_3'])